On one type of compactification of positive integers

TL;DR

This paper investigates a specific compactification of positive integers, demonstrating its isomorphism with a ring of remainder classes of polyadic integers, thus linking discrete number sets with compact algebraic structures.

Contribution

It introduces a new compact metric ring containing positive integers densely and proves its isomorphism with a ring of remainder classes of polyadic integers.

Findings

The compact metric ring contains positive integers densely.

The ring is isomorphic to a ring of remainder classes of polyadic integers.

Establishes a connection between discrete integers and compact algebraic structures.

Abstract

A compact metric ring containing the set of positive integers as dense subset is studied. It is proven that tis ring is isomorph with a ring of reminder classes of ring of polyadic integers.